Information transmittal, relativity and gravitation

Special relativity considered in [Albert Einstein, Zur Elektrodynamik der bewegte Körper, Ann. Phys. 17 (1905) 891–921], and gravitation, studied in a series of papers, notably in [Albert Einstein, Zum gegenwärtigen Stände des Gravitationsproblemen, Phys. Z. 14 (1913) 1249–1262], are further analyzed regarding the principle of relativity, gravitation, and the notion of mass. The energy relation derived by Einstein from the relativistic Maxwell equations is applied to potential energy W(x)W(x) of the gravitational field along the right line for which Einstein’s transformations are valid. This defines the intensity G(x)=dW/dx of the relativistic force of gravity along a right line of observation in the gravitational field. The force is proportional to the observed   acceleration according to the formula εG(x)=μξττ=μxttβ3 where μμ is the inert   mass in the second Newton’s law of motion and εε is the charge (mass) in the relativistic electromagnetic (gravitational) field. In everyday life, we see that all bodies visually fall under gravity (i.e. in a common gravitational field) with the same observed acceleration ξττξττ as if having equal inert and gravitational masses: μ/ε=1μ/ε=1, with respect to the synchronized time ττ. However, if the principle of relativity extended by Einstein to the case of the uniformly accelerated rectilinear motion is valid, then this relation should also be true with respect to xttxtt, that is, (μ/ε)β3=1(μ/ε)β3=1, in proper time tt of a still observer and of the carrying system (falling body), thus, depending on velocity vv at which the acceleration ξττξττ is measured. This means that the inert mass μμ and the gravitational mass εε can be considered equal only   at v=0v=0, and otherwise are related by the equation ε=μβ3≥με=μβ3≥μ, where Einstein’s calibration factor β=[1−(v/V)2]−0.5≥1,|v|0v>0, then the observed   gravitational mass εε is greater   than the inert mass μμ. The increase of mass is concurrent with the increase of tensions that at high velocities v→Vv→V induce overheating in the particle accelerators and colliders. To comply with the nature of observation, the information transmittal signals are incorporated in the Lorentz invariant of the 4D4D geometry, leading to the local invariants of relativistic dynamics that include gravitation and the speed of signals used in observation of moving bodies. With the same communication signals, those invariants hold for the synchronized time and coordinates of moving systems irrespective of their relative velocities. A procedure is developed for measurement and computation of the accelerations produced by variable gravitational and/or electromagnetic fields through the measurements of velocities of a moving body, so that the motion of the body and the field of forces acting on it can be fully identified. The results open new avenues for research in the theory of relativity and its applications.